Explanation Given Information: The provided function is, h ( x ) = e x 2 + 1 Formula used: First Derivative Test: Suppose that c is a critical point of the continuous function f and its derivative is defined for x close to, and on both sides of x = c . Then, determine the sign of the derivative to the left and the right of x = c . If f ′ ( x ) is positive to the left of x = c and negative to the right, then f has a maximum at x = c . If f ′ ( x ) is negative to the left of x = c and positive to the right, then f has a minimum at x = c . If f ′ ( x ) has the same sign on both sides of x = c , then f has neither a maximum nor a minimum at x = c . Stationary Points are the points in the interior of the domain where the derivative is zero. To locate stationary points set f ′ ( x ) = 0 and solve for x . Singular Points are the points in the interior of the domain where the derivative is not defined. To locate singular points, find the interior points x where f ′ ( x ) is not defined but f ( x ) is defined. Closed intervals contain end points but open intervals do not have end points. Calculation: Consider the provided function, h ( x ) = e x 2 + 1 Differentiate the function h ( x ) = e x 2 + 1 on both sides with respect to x as, h ′ ( x ) = 2 x e x 2 Now, locate the singular points by h ′ ( x ) = 0 to get, 2 x e x 2 = 0 Since, h ′ ( x ) = 0 for x = 0 . Thus, x = 0 is the stationary point. The equation h ' ( x ) = 2 x e x 2 is defined for all x

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 12, Problem 8RE

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To calculate: The exact location of the relative and absolute extrema of the function h(x)=ex2+1.

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Chapter 12, Problem 7RE

Chapter 12, Problem 9RE

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The exact location of the relative and absolute extrema of the function h ( x ) = e x 2 + 1 .

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To calculate: The exact location of the relative and absolute extrema of the function h(x)=ex2+1.

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Chapter 12 Solutions